Free IB Maths AA SL lesson: Unit circle & exact values
A ready-to-teach IB Maths AA SL lesson on Unit circle & exact values (Unit 3 · Geometry & Trigonometry): editable slides and teacher notes, free; a printable worksheet in 3 levels with answers for school plans. About 55 minutes.
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What's inside
- Slides (PowerPoint, editable) · freeabout 12 slides: do now, objectives, key ideas, a worked example step by step, “your turn”, practice QR code, exit ticket
- Teacher notes (PDF) · freelesson plan with timings, common mistakes, homework links
- Worksheet (PDF) · school plans6 questions, 26 marks: Fluency, Reasoning, Exam-style. Included with school plans and the teacher trial.
- Answers (PDF) · school plansthe answer to every worksheet question, from its mark scheme. Included with school plans and the teacher trial.
Learning objectives
- Unit Circle: Trig Ratios of Any Angle & Exact Values
- Exact Values in All Four Quadrants
- Given One Trig Ratio, Find the Others
Key ideas on the slides
- On the unit circle, the point at angle θ is (cos θ, sin θ), and tan θ = (sin θ)/(cos θ).
- Signs by quadrant (CAST): all positive in the first; sin in the second; tan in the third; cos in the fourth.
- Related angles: sin(π − θ) = sin θ, cos(π − θ) = −cos θ, sin(−θ) = −sin θ, cos(−θ) = cos θ.
- Exact values: sin π/6 = ½, sin π/4 = (√2)/2, sin π/3 = (√3)/2, tan π/4 = 1, tan π/3 = √3.
By the end of the lesson, students should be able to answer a question like: Write down the exact value of cos(4π/3).
Key vocabulary
- unit circle: The circle of radius 1 centred at the origin.
- quadrant: One of the four regions made by the axes.
- exact value: A value given with surds and fractions, not a decimal.
Common mistakes this lesson tackles
- Trigonometric equations: one solution only, and exact values not known. Sketch the graph over the given interval and count the solutions before you start. Learn the exact values for 0, π/6, π/4, π/3, π/2 and their related angles.
- Getting the sign wrong in the second, third or fourth quadrant.
- Mixing up sin π/6 and cos π/6.
- Giving a decimal when an exact value is asked for.
The worked example
Given sin θ = ⅗ and π/2 < θ < π, find the exact values of cos θ and tan θ.
- Quadrant 2: cosine and tangent are negative.
- Pythagorean identity: cos²θ = 1 − 9/25 = 16/25.
- Square root, negative in Q2: cos θ = −⅘.
- Tangent: tan θ = (3/5)/(−4/5) = −¾.
Tip: A 3-4-5 reference triangle is a valid alternative, provided you remember to apply the ASTC sign rules to the final answer.
Calculator tips
- Check exact values in radian mode; the calculator's exact display (S⇔D) shows surds.
Lesson plan
| 0–5 min | Do now: students write down what they remember about Arc length & sector area and Radian measure |
| 5–8 min | Share the learning objective and success criteria |
| 8–20 min | Teach: the worked example, step by step; students copy the method |
| 20–25 min | Your turn: 1 mini-whiteboard question; check every board before moving on |
| 25–42 min | Practise: the worksheet (6 questions in 3 levels, with school plans and the teacher trial) or the topic's practice questions online; move up a level after two right in a row |
| 42–47 min | Plenary: 1-question exit ticket; collect it to plan the next lesson |
For students: practise this topic
The worksheet's QR code opens the IB Maths AA SL Unit 3: The unit circle and exact values of trigonometric ratios practice questions.
What schools get
- Set this lesson as homework, marked by AI against the mark scheme, with every result in your markbook (with a School plan).
- This lesson's worksheet in three levels, with its answers, ready to print.
- Support, Core and Stretch versions and A/B copies of the worksheet from the full question bank, in the worksheet builder.
- Create lesson: this lesson rebuilt for your class's next scheme-of-work lesson, from the full bank.
School licences from €490 a year. Try everything free for 30 days as a teacher: no card.
Questions teachers ask
Is this lesson free?
The slides and the teacher notes are free to download with a free IB Math Revision teacher account (sign in with Google, Microsoft or email); no card. The printable worksheet in three levels and its answers are included with school plans and the free 30-day teacher trial.
Can I edit the slides?
Yes. The slides are an ordinary PowerPoint file: change, add or delete anything. They also open in Google Slides and Keynote. The logo and web address sit on the slide master, so your edits do not move them.
What do students use for homework?
The practice slide's QR code and web address take students to the IB Maths AA SL Unit 3: The unit circle and exact values of trigonometric ratios practice questions on ibmathrevision.com, where the free questions are open and the full bank comes with a plan.